The contractor building the new National Children's Hospital has submitted claims for extra costs.
The claims have yet to be adjudicated on to see if they are valid.
Currently, the project has a pricetag of €1.7 billion - almost three times the original expected cost.
Taoiseach Leo Varadkar has said the further claims now need to be examined.
Speaking in the Dáil this afternoon, he told TDs: "In terms of the National Children's Hospital, there's been no change to the Budget allocated in December 2018.
"The contractor has, however, submitted claims, and these have yet to be adjudicated.
"It's not unusual in a major construction project for a contractor to submit claims if they believe they've had to carry out work that was beyond the contract."
The Labour Party health spokesperson Alan Kelly said he believes the bill will top €2bn.
“Many months ago when I said quite strongly and emphatically that I believed that this hospital would end up going over €2bn,” he said.
“That was without talking about IT or necessarily the fit-out. The Taoiseach said I was exaggerating.
“Well I would like to ask the Taoiseach if he believes now that I was exaggerating – because it absolutely will.”
In September, it was revealed that the construction of the new National Children's Hospital is falling behind schedule.
The Health Service Executive (HSE) has warned that the project is facing delays which could affect critical timelines.
The hospital is due to open in April 2023.
